Adaptive Wide Angle, Warp or Punt?

Here is a 4 shot pano, camera on tripod, on Panosaurus Rex held in vertical position. EF-S 10-22 set at 14mm.
I can't get a good equilateral blend in PTgui or PS. This was the best I could do set to Equirectangular. The verticals are pretty good but of course, the whole inside is bulbous.
I tried my had with the Adaptive wide angle tool but got nowhere. All the options in the drop down menu, fisheye, etc. yielded results even worse than what I'm starting out with here.
Is this image beyond what that filter can correct? Somebody suggested I try the warp tool but I don't know how it works.
Thanks

I suspect the image capture would have been better with a longer focal length lens selected and more images to blend. It should help with some of the distortion you are seeing using a relatively wide angle lens.

Cannot offer any help with PTgui and its tools. But it you have to use the warp tool you will need to drag the handles highlighted with red circle in the attached image down to compensate. I put a horizontal guide line in for reference. In doing this you are also distorting other image elements by compressing. The image you see behind is your original, you are moving an awful lot of pixels here a long way which may prove a step too far. So better to get right in camera?